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- W2600757166 abstract "A Cayley graph $Ga=Cay(G,S)$ is said to be normal if $G$ is normal in $AutGa$. The concept of normal Cayley graphs was first proposed by M.Y.Xu in [Discrete Math. 182, 309-319, 1998] and it plays an important role in determining the full automorphism groups of Cayley graphs. In this paper, we investigate the normality problem of the connected arc-transitive pentavalent Cayley graphs with soluble vertex stabilizer on finite nonabelian simple groups. We prove that all such graphs $Ga$ are either normal or $G=A_{39}$ or $A_{79}$. Further, a connected arc-transitive pentavalent Cayley graph on $A_{79}$ is constructed. To our knowledge, this is the first known example of pentavalent 3-arc-transitive Cayley graph on finite nonabelian simple group which is non-normal." @default.
- W2600757166 created "2017-04-07" @default.
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- W2600757166 date "2017-02-19" @default.
- W2600757166 modified "2023-09-25" @default.
- W2600757166 title "Arc-transitive pentavalent Cayley graphs with soluble vertex stabilizer on finite nonabelian simple groups" @default.
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- W2600757166 doi "https://doi.org/10.48550/arxiv.1702.05754" @default.
- W2600757166 hasPublicationYear "2017" @default.
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